A complete bounded minimal cylinder in R^3

TL;DR

This paper extends Nadirashvili's 1996 work by constructing new complete minimal surfaces with annular conformal structure inside a ball in R^3, using generalized Runge's theorem techniques.

Contribution

It introduces a method to generate complete minimal surfaces with annular topology inside a ball, expanding the class of known minimal surfaces in R^3.

Findings

Constructed new complete minimal annuli inside a ball in R^3.

Generalized Runge's theorem techniques to minimal surface theory.

Expanded the understanding of minimal surfaces with complex conformal structures.

Abstract

In 1996, Nadirashvili used Runge's theorem to produce a complete minimal disc inside a ball in R^3. In this paper we generalize the techniques used by Nadirashvili to obtain new examples of complete minimal surfaces inside a ball in R^3, with the conformal structure of an annulus.